Basic Math Examples

$4 (\frac{1}{2} \cdot (a b)) + {(b - a)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{2} (a b)$ .

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Step 1.1.1

Combine $a$ and $\frac{1}{2}$ .

$4 (\frac{a}{2} b) + {(b - a)}^{2}$

Step 1.1.2

Combine $\frac{a}{2}$ and $b$ .

$4 \frac{a b}{2} + {(b - a)}^{2}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{a b}{2} + {(b - a)}^{2}$

Step 1.2.2

Cancel the common factor.

$2 \cdot 2 \frac{a b}{2} + {(b - a)}^{2}$

Step 1.2.3

Rewrite the expression.

$2 (a b) + {(b - a)}^{2}$

Step 1.3

Rewrite ${(b - a)}^{2}$ as $(b - a) (b - a)$ .

$2 a b + (b - a) (b - a)$

Step 1.4

Expand $(b - a) (b - a)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$2 a b + b (b - a) - a (b - a)$

Step 1.4.2

Apply the distributive property.

$2 a b + b \cdot b + b (- a) - a (b - a)$

Step 1.4.3

Apply the distributive property.

$2 a b + b \cdot b + b (- a) - a b - a (- a)$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Multiply $b$ by $b$ .

$2 a b + b^{2} + b (- a) - a b - a (- a)$

Step 1.5.1.2

Rewrite using the commutative property of multiplication.

$2 a b + b^{2} - b a - a b - a (- a)$

Step 1.5.1.3

Rewrite using the commutative property of multiplication.

$2 a b + b^{2} - b a - a b - 1 \cdot - 1 a \cdot a$

Step 1.5.1.4

Multiply $a$ by $a$ by adding the exponents.

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Step 1.5.1.4.1

Move $a$ .

$2 a b + b^{2} - b a - a b - 1 \cdot - 1 (a \cdot a)$

Step 1.5.1.4.2

Multiply $a$ by $a$ .

$2 a b + b^{2} - b a - a b - 1 \cdot - 1 a^{2}$

Step 1.5.1.5

Multiply $- 1$ by $- 1$ .

$2 a b + b^{2} - b a - a b + 1 a^{2}$

Step 1.5.1.6

Multiply $a^{2}$ by $1$ .

$2 a b + b^{2} - b a - a b + a^{2}$

Step 1.5.2

Subtract $a b$ from $- b a$ .

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Step 1.5.2.1

Move $b$ .

$2 a b + b^{2} - a b - a b + a^{2}$

Step 1.5.2.2

Subtract $a b$ from $- a b$ .

$2 a b + b^{2} - 2 a b + a^{2}$

Step 2

Combine the opposite terms in $2 a b + b^{2} - 2 a b + a^{2}$ .

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Step 2.1

Subtract $2 a b$ from $2 a b$ .

$b^{2} + 0 + a^{2}$

Step 2.2

Add $b^{2}$ and $0$ .

$b^{2} + a^{2}$